A new adaptive restart for GMRES($m$) method

Abstract

GMRES($m$) is a Krylov subspace method for solving nonsymmetric linear systems of equations. The difficulty of this method lies in choosing the appropriate restart cycle $m$. We propose a new strategy for the adaptive restart for GMRES($m$) which is based on using the difference of the Ritz and harmonic Ritz values. We also report on numerical experiments which show that this new approach is both effective and robust.